A solid body dynamic model in a magnetic field

An absolutely solid asymmetric body-magnet moves relative to a stationary pole in a stationary homogeneous magnetic field of constant intensity. The magnetic center of the body is located in one of the main planes of its ellipsoid of inertia, assigned to this pole. The motion of a body is considered as non-linear oscillations occurring near its position of stable equilibrium under the assumption that such an equilibrium exists. Analytical transformations of the system of equations of oscillation of a body with its reduction to a canonical form and to a special form according to A. Lyapunov are carried out. The possibility of reducing the system is noted. The conditions for the existence of resonance in the linear subsystem of the equations of motion are obtained, presented in the form of relations linking the inertial and magnetic parameters of the body.